Finite Group Databasebeta

← #28335437

Subgroups — #28335437

Order 13696.

238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293258C211yesmaximal, characteristic
2#20292785C212yesmaximal
3#20292547C211yesmaximal, characteristic
4#20292365C212yesmaximal
5#324×C107C211yesmaximal, characteristic
6C22×Dic214C2211yescharacteristic
7C2×Dic428—22no—
8#16812108—22no—
9#16812100—22no—
10#16812088—21no—
11#16812088C2212yes—
12#16812068—21no—
13C2×Dic107⋊C4—21no—
14#16812034—22no—
15C107⋊#95—21no—
16C107⋊#95C2211yescharacteristic
17C2×C4⋊C4×C107C2211yescharacteristic
18C22⋊C8×C107C2212yes—
19C2×Dic214—22no—
20C2×Dic214—21no—
21C2×Dic214—42no—
22C2×Dic214D412yes—
23C22×Dic107—21no—
24C22×Dic107—21no—
25Dic428—44no—
26C4⋊Dic107—21no—
27C4⋊Dic107—21no—
28C4⋊Dic107—21no—
29C4⋊Dic107D412yes—
30Dic107⋊C4—22no—
31Dic107⋊C4—22no—
32Dic107⋊C4—42no—
33C22⋊Dic107—22no—
34C4×Dic107—22no—
35C22×C4×C107D411yescharacteristic
36C22×C4×C107D411yescharacteristic
37C22×C4×C107C2311yescharacteristic
38C2×C8×C107—22no—
39C4⋊C4×C107—22no—
40C23×C107C2×D411yescharacteristic
41C2×C4×C107—21no—
42C2×C4×C107—21no—
43C2×C4×C107—21no—
44C2×C4×C107—41no—
45C2×C4×C107—41no—
46C2×C4×C107Q1612yescomplemented
47C2×C4×C107C2×D412yes—
48C2×Dic107—22no—
49C2×Dic107—22no—
50C2×Dic107—22no—
51C2×Dic107—22no—
52C2×Dic107—41no—
53C2×Dic107—41no—
54C2×Dic107—41no—
55C2×Dic107—41no—
56Dic214—24no—
57Dic214—42no—
58Dic214—42no—
59Dic214—81no—
60C8×C107—42no—
61C22×C107—21no—
62C22×C107—21no—
63C22×C107#12011yescharacteristic
64C22×C107C2×Q1611yescharacteristic
65C22×C107#13711yescharacteristic
66C4×C107—22no—
67C4×C107—22no—
68C4×C107—41no—
69Dic107—42no—
70Dic107—42no—
71Dic107—42no—
72Dic107—42no—
73C2×C107—21no—
74C2×C107—21no—
75C2×C107#45111yescharacteristic
76C2×C107#45611yescharacteristic
77C2×C107B(4,𝔽2)11yescharacteristic
78#1605—1071nomaximal, Sylow
79C107#160511yescharacteristic, complemented, Sylow
80#544—1071no—
81#451—1072no—
82#395—1071no—
83#328—1072no—
84#324D10711yescharacteristic
85C22×Q8—1071no—
86C2×Q16—2142no—
87C4⋊Q8—2142no—
88#125—2142no—
89C22⋊Q8—1072no—
90C22⋊Q8—2141no—
91#117—2141no—
92C2×C4⋊C4—2141no—
93C2×C4⋊C4C2×D10711yescharacteristic
94#103—2142no—
95C22⋊C8C2×D10712yes—
96#95—1071no—
97#95—2141no—
98C2×Q8—1072no—
99C2×Q8—4282no—
100C2×Q8—2141no—
101C2×Q8—2142no—
102C22×C4—2141no—
103C22×C4—2141no—
104C22×C4D42811yescharacteristic
105C22×C4D42811yescharacteristic
106C22×C4C22×D10711yescharacteristic
107Q16—4284no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—1072no—
111C4⋊C4—4282no—
112C4⋊C4—2141no—
113C4⋊C4—2141no—
114C4⋊C4—2141no—
115C4⋊C4—2142no—
116C4⋊C4—2142no—
117C22⋊C4—2142no—
118C42—2142no—
119C23C2×D42811yescharacteristic
120Q8—8561no—
121Q8—4282no—
122Q8—4282no—
123Q8—2144no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—4281no—
130C2×C4—4281no—
131C2×C4—4281no—
132C2×C4—4281no—
133C2×C4—2142no—
134C2×C4—2142no—
135C2×C4—2142no—
136C2×C4—2142no—
137C2×C4Dic42812yescomplemented
138C2×C4D4×D10712yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#1681207911yescharacteristic
143C22C2×Dic42811yescharacteristic
144C22#1681214211yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—4282no—
149C4—4282no—
150C4—4282no—
151C4—4282no—
152C2—21no—
153C2—21no—
154C2#2029278511yescharacteristic
155C2#2029281211yescharacteristic
156C2#2029281511yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#324×C107C2
socleC22×C107#120
prime radicalC23×C107C2×D4
hypercenter#324D107
hypocenterC107#1605
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
46. C2×C4×C107Q16semidirect
79. C107#1605semidirect
137. C2×C4Dic428semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202932582
#202927852
#202925472
#202923652
#324×C1072
#1605107